The Integral

Abstract

In this chapter, we begin the study of the subject of differential equations, which is one of the common ties binding together all areas of science and engineering, and it would be hard to overstate its importance. We have been preparing for this chapter for a long time, starting from the beginning with Chapter A very short course in Calculus, through all of the chapters on functions, sequences, limits, real numbers, derivatives and basic differential equation models. So we hope the gentle reader is both excited and ready to embark on this new exploration.

Keywords

Summing

The two questions, the first that of finding the description of the curve from its elements, the second that of finding the figure from the given differences, both reduce to the same thing. From this it can be taken that the whole of the theory of the inverse method of the tangents is reducible to quadratures. (Leibniz 1673)